Applicability of Kotel'nikov's theorem to discrete measurement techniques

Abstract

1. The linear interpolation method requires a higher (by a factor of 1.4) rate of transformation for signals of the simplest form compared with approximation functions of the type of sinx or sin x/x, but it reduces that rate to hundredths and thousandths of that required for the latter functions in transforming variables of a more complex form, for instance, of the exponential type. 2. Kotel'nikov's theorem applies to approximations by means of a function of the type of sin x/x, hence it is not suitable for discrete measurements for the reasons given above; moreover, its application makes it difficult to obtain the values of the measured variable between two adjacent discrete readouts. 3. A linear approximation appears to be sufficiently suitable and convenient for discrete measurements of continuous variables; its application does not require additional computations, devices or gauges, which would have been required for any other approximating function. 4. When signals approaching a harmonic form are measured by the discrete method, the main propositions of Kotel'nikov's theorem hold if the highest frequency fs of the measured signal spectrum is taken to be the harmonic frequency which must be evaluated in order to obtain a discrete representation of a harmonic pulse signal with a given accuracy.